Polynomial Function and Synthetic DivisionAleczQ1414
This file is about Polynomial Function and Synthetic Division. A project passed to Mrs. Marissa De Ocampo. Submitted by Group 6 of Grade 10-Galilei of Caloocan National Science and Technology High School '15-'16
Continuity, Removable Discontinuity, Essential Discontinuity. These slides accompany my lectures in differential calculus with BSIE and GenENG students of LPU Batangas
Polynomial Function and Synthetic DivisionAleczQ1414
This file is about Polynomial Function and Synthetic Division. A project passed to Mrs. Marissa De Ocampo. Submitted by Group 6 of Grade 10-Galilei of Caloocan National Science and Technology High School '15-'16
Continuity, Removable Discontinuity, Essential Discontinuity. These slides accompany my lectures in differential calculus with BSIE and GenENG students of LPU Batangas
Solving AIEEE problems fast is fun. We claim that 30% of AIEEE problems consists of such problems only and show you how to save your time for the problems where you may be losing double of your time. All you need to know is aware of these tricks
Properties of coordination complexes CompleteChris Sonntag
Application of Crystal Field Theory to explain the main physico-chemical properties of Transition Metal Complexes (not organometalic)
In the first part we use this theory to explain several characteristics of coordination complexe.
To download -https://clk.ink/MS2T
this will lead to a google drive link./
its a ppt based on the topic no. system.
it covers all the basics of ninth class cbse.
HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2HIGHWAY AND TRANSPORT ENGINERING EXAM AND ANSWER-2
Complex analysis and its application
2.Contents,Complex number
Different forms of complex number
Types of complex number
Argand Diagram
Addition, subtraction, Multiplication & Division
Conjugate of Complex number
Complex variable
Function of complex variable
Continuity
Differentiability
Analytic Function
Harmonic Function
Application of complex Function
3.Complex Number,For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8 are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as -3 and-5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits.
All numbers are imaginary (even "zero“ was contentious once). Introducing the square root(s) of minus one is convenient because
all n-degree polynomials with real coefficients then haven roots, making algebra "complete";
it saves using matrix representations for objects that square to-1 (such objects representing an important part of the structure of linear equations which appear in quantum mechanics ,heat,diffusion,optics,etc) .The hottest contenders for numbers without purpose are probably the p-adic numbers (an extension of the rationales),and perhaps the expiry dates on army ration packs.
4.Complex Number is defined as an ordered pair of real number X & Y and is denoted by (X,Y)
It is also written as 𝒛=𝒙,𝒚=𝒙+𝒊𝒚,where 𝑖^2=−1
𝑥 is called Real Part of z and written as Re(z)
Y is called imaginary part of z and written as Im(z).
-If R(z) = 0 then 𝑧=𝑖𝑦, is called Purely Imaginary Number.
-If I(z) = 0 then 𝑧=𝑥, is called Purely Real Number.
-Here 𝑖can be written as (0, 1) = 0 ±1𝑖
Note:-−𝒂= 𝑎−1=𝑖𝑎
-If 𝑧=𝑥+𝑖𝑦is complex number then its conjugate or complex conjugate is defined as 𝒛=𝒙−𝒊𝒚.
5.DIFFERENT FORMS OF COMPLEX NUMBER
Cartesian or Rectangular Form :-𝑧=𝑥+𝑖𝑦
Polar Form :-𝑧=𝑟(cos𝜃+𝑖sin𝜃) 𝑜𝑟 𝑧=𝑟∠𝜃
Exponential Form :-𝑧=𝑟𝑒^𝑖𝜃
MODULUS & ARGUMENT OF COMPLEX NUMBER
Modulus of complex number (|z|) OR mod(z) OR 𝑟=√(𝑋^2+𝑌^2 )
Argument OR Amplitude of complex number (𝜃) OR arg (𝑧) OR amp(z)=tan^(−1)(𝑥/𝑦)
6.Argand Diagram
Mathematician Argand represent a complex number in a diagram known as Argand diagram. A complex number x+iy can be represented by a point P whose co–ordinate are (x,y).The axis of x is called the real axis and the axis of y the imaginary axis. The distance OP is the modulus and the angle, OP makes with the x-axis, is the argument of x+iy.
7.Addition of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)+(c+id)=(a+c)+i(b+d)
Procedure: In addition of complex numbers we add real parts with real parts and imaginary parts with imaginary parts.
8.Subtraction of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)-(c+id)=(a-c)+i(b-d)
Procedure: In subtraction of complex numbers we subtract real parts w
Aplikasi Bilangan Kompleks - Analisis Sinyal [PAPER]Ghins GO
Check out!
Website : https://ghinsblog.blogspot.com
Youtube : Ghins GO Math
APLIKASI BILANGAN KOMPLEKS
BAB 1 Pendahuluan
1. Latar belakang
2. Rumusan Masalah
3. Tujuan
BAB 2 Pembahasan
1. Bilangan Kompleks
2. Sinyal
BAB 3 Aplikasi
1. Analisis Sinyal
2. Analisis Fourier
3. Analisis Frekuensi Sinyal Periodik Waktu Diskrit
4. Penerapan Analisis Sinyal
BAB 4 Kesimpulan
DAFTAR PUSTAKA
[1] Gumilang, Muhammad. 2015. "Aplikasi Bilangan Kompleks dalam Analisis Sinyal". https://adoc.pub/aplikasi-bilangan-kompleks-dalam-analisis-sinyal.html, diakses 14 Mei 2021 pukul 18.11.
[2] Haryono, Stefanus Agus. 2015."Penggunaan Bilangan Kompleks dalam Pemrosesan Signal".https://pdfslide.tips/documents/penggunaan-bilangan-kompleks-dalam-pemrosesan-signalinformatikasteiitbacidrinaldimuniraljabargeometri2015aa.html, diakses 13 Mei 2021 pukul 20.37.
[5] Ratnadewi. dkk. 2019. "MATEMATIKA TEKNIK". Bandung: Rekayasa Sains.
Selengkapnya:
https://ghinsblog.blogspot.com/2021/08/variabel-kompleks-aplikasi-bilangan.html
Complex Number,
Mathematical Requirement,
Geometrical Requirement,
Conventions,
Representation,
Modulus And Argument,
Real Vs Complex Numbers ,
Purely Real Complex Number ,
Purely Imaginary Complex Number ,
Equality Between Two Complex Numbers ,
Operation on Complex Number ,
Polar Form of Complex Number ,
About Other Than Origin ,
Properties of Complex Number ,
Logarithm of Complex Number ,
Parametric Conversion,
De Moivre’s Theorem ,
Properties of the Arguments ,
Roots of a Complex Number ,
Analytical Complex Numbers ,
Limit & Continuity,
Poles & Zeros,
Complex Derivative ,
Complex Integration ,
Mczee explains Conservation of Linear Momentumyoumarks
Our Mczee again stuck in a climbing problem. This time with a balloon. But he learns a lot of physics with this experience. And guess who helps in understanding the stuff?
Chimpoo and McZee use basic principles of Physics to easily climb a rope. Must to read to understand laws of Physics. Please do not include these presentations without our prior permission.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.